Laplacian in Slanted Coordinates

[mathskier]

Whoops, I figured it out!

 

[Dick]

Homework Statement

Determine ∇²F in a coordinate system with u and v, where u=y-x and v=y.

Homework Equations

The Attempt at a Solution

I think that this is ∇²F= 2 (∂²F/∂r² + ∂²F/(∂r ∂s))+∂²/∂s². But I don't know how to check this... Is it correct?

Well, how did you get it? It can't be right, since the derivatives are with respect to r and s (whatever they are), not u and v.